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VOL. 5 | 2009 Uniform Central Limit Theorems for pregaussian classes of functions
Dragan Radulović, Marten Wegkamp

Editor(s) Christian Houdré, Vladimir Koltchinskii, David M. Mason, Magda Peligrad


We study weak convergence of general (smoothed) empirical processes indexed by classes of functions $\mathcal{F}$ under minimal conditions. We present a general result that, applied to specific situations, enables us to prove uniform central limit theorems under P-pregaussian assumption on $\mathcal{F}$ only.


Published: 1 January 2009
First available in Project Euclid: 2 February 2010

zbMATH: 1243.60026
MathSciNet: MR2797942

Digital Object Identifier: 10.1214/09-IMSCOLL507

Keywords: Empirical processes , Fourier series density estimator , kernel density estimator , uniform central limit theorems , weak convergence

Rights: Copyright © 2009, Institute of Mathematical Statistics


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